CN110109415B - Multi-grid cutter shaft optimization method based on density clustering - Google Patents

Multi-grid cutter shaft optimization method based on density clustering Download PDF

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CN110109415B
CN110109415B CN201910341825.2A CN201910341825A CN110109415B CN 110109415 B CN110109415 B CN 110109415B CN 201910341825 A CN201910341825 A CN 201910341825A CN 110109415 B CN110109415 B CN 110109415B
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grid
cutter shaft
points
clustering
coarse
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CN110109415A (en
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陈吉红
李振瀚
杨方召
张玉明
胡鹏程
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Huazhong University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35349—Display part, programmed locus and tool path, traject, dynamic locus

Abstract

The invention belongs to the technical field related to milling and discloses a density clustering-based multi-grid cutter shaft optimization method, which comprises the following steps: (1) standardizing the coordinates of the tool contact points to avoid the problem of unreasonable clustering results caused by unreasonable arc length variation values; (2) carrying out density clustering on the tool contact subjected to the standardized processing; (3) calculating a coarse grid corresponding to the cutter contact point according to the obtained clustering family, and optimizing a cutter shaft of the coarse grid point based on the coarse grid; meanwhile, fine grids are established between two adjacent coarse grid points, and the cutter shaft of the fine grid points is optimized based on each fine grid, so that the optimization of the cutter shaft is completed. According to the invention, the tool contacts are subjected to standardization treatment and density clustering in sequence, and then the tool shafts optimized by the coarse grid and the fine grid are integrated to obtain the integrally optimized tool shaft, so that the convergence rate of the algorithm can be greatly improved without reducing the tool shaft optimization effect, and the practicability is strong.

Description

Multi-grid cutter shaft optimization method based on density clustering
Technical Field
The invention belongs to the technical field related to milling, and particularly relates to a multi-grid cutter shaft optimization method based on density clustering.
Background
Compared with three-axis numerical control machining, the five-axis numerical control machining can ensure better surface quality and higher machining efficiency, and at present, most of complex curved surface parts are machined by using the five-axis numerical control. Common complex curved surface parts include airplane bodies, propeller blades, mobile phone mold profile curved surfaces, turbine blades, automobile bodies and the like. In multi-axis numerical control machining, cutter shaft vector optimization is a very challenging problem, and the optimization effect depends on an optimization model and is related to a solution algorithm of the optimization model. The same cutter axis vector optimization model uses different solving methods, and finally planned cutter axis vector fields may be completely different. Different optimization model solving methods have different degrees of influence on the iteration speed and the optimization precision of the algorithm, and the finding of the cutter shaft optimization model solving algorithm which is high in solving efficiency and does not influence the convergence precision of the algorithm has important significance on the research of multi-axis cutter shaft optimization.
At present, some research has been made by those skilled in the art, for example, patent 201810745901.1 discloses a multi-objective constraint-based cutter shaft vector optimization method and system, which directly use a constraint optimization method to solve a cutter shaft optimization model, when cutter shaft optimization is performed on a finish machining trajectory, although a high-quality multi-axis machining trajectory can be obtained, since the number of trajectories is large, the solution of the cutter shaft optimization model is extremely time-consuming, and if the solution is integrated into CAM software, the performance of the software is greatly affected. Accordingly, there is a need in the art to develop a multi-grid cutter shaft optimization method based on density clustering with a high speed.
Disclosure of Invention
Aiming at the defects or improvement requirements in the prior art, the invention provides a multi-grid cutter shaft optimization method based on density clustering, which is based on the characteristics of the existing cutter shaft optimization and researches and designs a multi-grid cutter shaft optimization method based on density clustering with better speed. According to the optimization method, the cutter contacts are clustered, grids are divided according to the clustered clusters, then the cutter shafts of the coarse grids and the fine grids are optimized respectively, and the cutter shafts optimized by the coarse grids and the fine grids are integrated to obtain the cutter shaft after the whole optimization.
In order to achieve the above object, according to an aspect of the present invention, there is provided a multi-grid cutter shaft optimization method based on density clustering, the optimization method including the steps of:
(1) carrying out density clustering on the knife contact points subjected to the standardized processing, and specifically comprising the following steps:
s2.1, based on the tool contact set D ═ { CC ═1,CC2,...,CCnDetermining neighborhood parameters {, MinPts }, wherein the neighborhood parameters represent neighborhood radius, MinPts represents the number of points contained in the neighborhood radius range, and n is the number of contact points; next, a set of core points is initialized
Figure BDA0002040974080000021
S2.2, sample CC when j is 1,2, …, n, respectivelyjField N of(CCj) If | N(CCj) If | ≧ MinPts, the sample CCjAdding core point set omega-omega ∪ (CC)j) In which N is(CCj)＝{CCi∈D|DIST(CCi,CCj)≤}，
Figure BDA0002040974080000022
dis(CCk,CCk+1) Representing the Euclidean distance of adjacent CC points, and the knife contact is called the CC point for short; then, initializing a cluster family number k equal to 0 and initializing an unvisited sample set equal to D;
s2.3, judging whether the core set omega is empty, if not, turning to the step S2.4, otherwise, executing the step S2.6;
s2.4, recording the current sample set which is not visitedoldAnd randomly selecting a core object o ∈ omega, and initializing a queue Q<o>(ii) a Then, after solving the difference set \ o } and assigning value, judging
Figure BDA0002040974080000023
If so, go to step S2.5, otherwise go to step S7;
s2.5, taking out the first sample Q in the queue Q, and judging | N(q) | is greater than MinPts, if yes, go to step S2.6, otherwise go to step S2.4;
s2.6, let Δ be N(Q) ∩, adding the samples in the delta into a queue Q, solving the difference set \ delta and assigning to the difference set \ delta, and enabling k to be k +1 to generate a cluster Ck＝old\ f; meanwhile, the difference set omega \ C is solvedkAnd assigning the value to omega, and further outputting clustering division C ═ C1,C2,...,Ck}；
(2) Calculating a coarse grid corresponding to the cutter contact point according to the obtained clustering family, and optimizing a cutter shaft of the coarse grid point based on the coarse grid; meanwhile, fine grids are established between two adjacent coarse grid points, and the cutter shaft of the fine grid points is optimized based on each fine grid, so that the optimization of the cutter shaft is completed.
Further, the optimization of the tool setting contact comprises the following steps: first, calculate the knife separatelyPoint set of contact point CC D ═ CC1,CC2,...,CCnMean and standard deviation of x, y, z axis coordinates Std; then, it is determined whether the variance Std is greater than 1, and if so, the CC point set D is set to { CC ═ CC1,CC2,...,CCnCoordinate according to formula
Figure BDA0002040974080000031
Finishing the standardization, wherein c is a coordinate value before the standardization; v is a normalized coordinate value; otherwise, let v equal const and end, where const is a constant.
Further, an arbor optimization model is adopted to optimize the arbor of the coarse grid point based on the coarse grid, and the expression of the arbor optimization model is as follows:
Figure BDA0002040974080000032
Figure BDA0002040974080000033
Figure BDA0002040974080000034
wherein the content of the first and second substances,
Figure BDA0002040974080000035
representing coarse grid points
Figure BDA0002040974080000036
A cutter shaft;
Figure BDA0002040974080000037
representing coarse grid points
Figure BDA0002040974080000038
Positioning a cutter shaft; w is a weight coefficient;
Figure BDA0002040974080000039
representing coarse grid points
Figure BDA00020409740800000310
And coarse grid points
Figure BDA00020409740800000311
A distance measure therebetween;
Figure BDA00020409740800000312
representing coarse grid points
Figure BDA00020409740800000313
The preferred direction of the knife shaft;
Figure BDA00020409740800000314
representing coarse grid points
Figure BDA00020409740800000315
The preferred direction of the knife shaft;
Figure BDA00020409740800000316
indicating cutter shaft
Figure BDA00020409740800000317
The minimum boundary of the anteversion angle range of (1);
Figure BDA00020409740800000318
indicating cutter shaft
Figure BDA00020409740800000319
The maximum boundary of the anteversion angle range of (1);
Figure BDA00020409740800000320
is a knife shaft
Figure BDA00020409740800000321
The forward rake angle of (1);
Figure BDA00020409740800000322
is a knife shaft
Figure BDA00020409740800000323
The roll angle of (d); const denotes a constant.
Further, the chord length of the coarse grid point during cutter shaft optimization is calculated by adopting the following formula:
Figure BDA00020409740800000324
wherein lk,k+1Representing the euclidean distance between adjacent CC points.
Further, an arbor optimization model is used to optimize the arbor at the fine grid points based on each fine grid, and the expression of the arbor optimization model is as follows:
Figure BDA0002040974080000041
Figure BDA0002040974080000042
Figure BDA0002040974080000043
wherein A isj+1Representing fine grid points CCj+1A cutter shaft; a. thejIndicates coarse grid point CCjPositioning a cutter shaft; w is a weight coefficient; lj+1，jRepresenting neighbouring fine grid points CCjAnd fine grid point CCj+1The euclidean distance between; mjRepresenting fine grid points CCjThe preferred direction of the knife shaft; mj+1Representing fine grid points CCj+1The preferred direction of the knife shaft;
Figure BDA0002040974080000044
showing the knife axis AjThe minimum boundary of the anteversion angle range of (1);
Figure BDA0002040974080000045
showing the knife axis AjThe maximum boundary of the anteversion angle range of (1); thetajIs a knife shaft AjThe forward rake angle of (1);
Figure BDA0002040974080000046
is a knife shaft AjThe roll angle of (d); const denotes a constant.
Further, the method comprises, among others,
Figure BDA0002040974080000047
const is 0, w is 4; and the head and tail cutter shafts are fixed in the optimized direction of the cutter shaft, and then the cutter shaft optimization model is solved by using a constraint optimization method to obtain the cutter shaft at the optimized fine grid point.
Further, the calculation of the coarse mesh comprises the following steps:
s3.1, replacing the samples in the obtained clustering group division C with a sequence corresponding to the samples, setting the initial traversal times i to be 1, and setting the maximum value in each clustering group to be MaxiMinimum value of MiniThe number of elements is NumiThe initial Grid division is { G ═ G }1,Gn}，G1Is the sequence of the first CC site, GnIs the sequence of the last CC site;
s3.2, judging whether i is not greater than k, if so, turning to the step S3.3, otherwise, turning to the step S3.6;
s3.3, calculating a clustering cluster CiMin of (1)iMax, MaxiAnd calculates Grid-Grid ∪ { Min ═ Gridi,Maxi}; at the same time, Max is judgedi-MiniIf n is true, go to step S3.4 if yes, otherwise go to step S3.5;
s3.4, clustering the clusters CiSorting in ascending order, traversing CiFinding two discontinuous sequence indexes1And Index2And calculate Grid ∪ { Index ═ Grid1,Index2}；
S3.5, let i ═ i +1, and go to step S3.2;
s3.6, and meanwhile, performing ascending sequencing on the Grid to obtain a Grid sequence Grid (g) of the Grid sequence1,g2,...,gp}；
S3.7, processing grid sequence Grindidex ═ g1,g2,...,gpA continuous grid sequence in (c) } toObtaining the final coarse grid
Figure BDA0002040974080000051
Further, when i ═ 2, 3.., p-1, all satisfied g are calculated and removedi-g i-11 and gi+1-giNot equal to 1 and gi-gi-1Not equal to 1 and gi+1-giGrid sequence g formed simultaneously with 1iTo obtain the final coarse grid
Figure BDA0002040974080000052
Generally, compared with the prior art, the multi-grid cutter shaft optimization method based on density clustering provided by the invention has the following beneficial effects:
1. according to the invention, density clustering is carried out on the cutter contacts, grid division is carried out on the basis of clustering, the region with dense CC points can be divided into the coarse grids, the problem that the change rate of the cutter shaft after optimization generates large discontinuous mutation in the region with large curvature due to sectional optimization is avoided, the optimization effect of the cutter shaft is ensured, and the optimization speed is improved.
2. When the method is used for density clustering, the distance between two nonadjacent CC points is calculated by calculating the sum of the chord lengths of all adjacent CC points between the two CC points to be the distance between the two nonadjacent CC points instead of directly calculating the Euclidean distance between the two nonadjacent CC points, so that the positions of the CC points in each cluster on the track are adjacent.
3. The invention also carries out standardization processing on the tool contact, selectively carries out standardization processing on the coordinate value with larger standard deviation when carrying out standardization processing on the coordinate of the CC point, can ensure that the algorithm can adapt to different cases, avoids the problem that the clustering result is unreasonable due to unreasonable variation value caused by the chord length between adjacent CC points due to undersize standard deviation, and improves the robustness of the algorithm.
4. The invention adopts a multi-grid optimization method to optimize the cutter shaft, can greatly improve the convergence rate of the algorithm, has important significance for improving the performance of CAM software, and has simple flow and easy implementation.
Drawings
FIG. 1 is a schematic flow chart of a multi-grid cutter shaft optimization method based on density clustering according to the present invention;
FIG. 2 is a schematic structural diagram of an arbor vector in actual machining in numerical control machining constructed by the density clustering-based multi-grid arbor optimization method in FIG. 1;
FIG. 3 is a schematic diagram of a circle of tool path during the fine machining of a turbine blade constructed by the density clustering-based multi-grid cutter shaft optimization method in FIG. 1;
FIG. 4 is a schematic diagram of a tool contact trajectory after tool contacts are standardized according to the density clustering-based multi-grid tool axis optimization method in FIG. 1;
FIG. 5 is a schematic illustration of cluster families generated by density clustering of the blade contacts in FIG. 4;
FIG. 6 is a schematic diagram of an optimized mesh generated by the density clustering based multi-mesh arbor optimization method of FIG. 1 according to the cluster families of FIG. 5;
fig. 7 is a schematic diagram of a knife shaft constructed by the density clustering-based multi-grid knife shaft optimization method in fig. 1 after coarse grid knife shaft optimization:
FIG. 8 is a schematic diagram of the multi-grid arbor optimization method based on density clustering in FIG. 1 for arbor optimization of a fine grid of arbor;
FIG. 9 is a schematic diagram of a circle of trajectory constructed by the density clustering-based multi-grid cutter shaft optimization method in FIG. 1 after cutter shaft optimization;
fig. 10 is a schematic diagram of the cutter shaft change rate before and after optimization by using the density clustering-based multi-grid cutter shaft optimization method in fig. 1.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to fig. 1 and fig. 2, the method for optimizing a multi-grid cutter shaft based on density clustering mainly includes the following steps:
step one, carrying out standardization processing on the tool contact point coordinates to avoid the problem that the clustering result is unreasonable due to unreasonable arc length variation values.
Referring to fig. 4, the standardization of the tool setting contact specifically includes the following steps:
(1) respectively calculating point set D ═ CC of knife contact point CC1,CC2,...,CCnMean and standard deviation of the x, y, z-axis coordinates Std.
(2) And (4) judging whether the variance Std is larger than 1, if so, executing the next step, and otherwise, turning to the step (4).
(3) CC Point set D ═ CC1,CC2,...,CCnThe coordinates are normalized as follows and then end.
Figure BDA0002040974080000071
Wherein c is a coordinate value before normalization; v is a normalized coordinate value.
(4) Let v be const, where const denotes an arbitrary constant, and end.
In the embodiment, the tool contact point is referred to as a CC point for short, and refers to a position point where a workpiece curved surface and a tool curved surface are tangent in the process of milling the workpiece curved surface by the tool; the tool contact point trajectory, i.e., the CC trajectory, is a collection of line segments in which all CC points are connected in a certain manner, called the tool contact point trajectory, and the direction of the tool axis vector may be determined by the rake angle and the roll angle. FIG. 3 shows a circle of CC tracks generated during the finishing of a turbine blade; a tool location point, referred to as CL point for short, is a positioning reference point of a tool, and for various milling tools, the intersection point of the axis of the tool and the bottom end of the tool is generally taken; the tool location point track is the CL track, and the collection of line segments connecting all the CL points in a certain way is called the tool location point track.
And step two, performing density clustering on the tool contact points subjected to the standardization treatment.
Referring to fig. 5, clustering the density of tool setting contacts specifically includes the following steps:
s2.1, based on CC point set D ═ { CC1,CC2,...,CCnDetermine neighborhood parameters, MinPts, where neighborhood radius is represented, and MinPts represents the number of points contained within the neighborhood radius.
S2.2, initializing a core point set
Figure BDA0002040974080000081
S2.3, sample CC when j is 1,2, …, n, respectivelyjField N of(CCj) If | N(CCj) If | ≧ MinPts, the sample CCjAdding core point set omega-omega ∪ (CC)j) In which N is(CCj)＝{CCi∈D|DIST(CCi,CCj)≤}，
Figure BDA0002040974080000082
dis(CCk,CCk+1) Representing the euclidean distance of neighboring CC points.
S2.4, initialize cluster family number k is 0, initialize unaccessed sample set D.
And S2.5, judging whether the core set omega is empty, if not, turning to the step S2.6, otherwise, executing the step S2.15.
S2.6, recording a current unvisited sample set:old＝。
s2.7, a core object o is randomly selected to form an omega, and a queue Q is initialized to be < o >.
S2.8, solving the difference set \ o and assigning values to the difference set.
S2.9, judgment
Figure BDA0002040974080000083
If not, go to step S2.10, if yes, otherwise go to step S2.13.
S2.10, taking out the first sample Q in the queue Q.
S2.11, judging | N(q) | is greater than MinPts, if yes, go to step S2.12, otherwise go to step S2.9.
S2.12, let Δ be N(Q) ∩, adding the samples in delta to queue Q, solving for the difference set \ delta and assigning to the difference set \ delta.
S2.13, let k be k +1 to generate cluster Ck＝old\。
S2.14, solving for difference set omega \ CkAnd assigned to Ω and go to step S2.5.
S2.15, outputting clustering division: c ═ C1,C2,...,Ck}。
In this embodiment, the neighborhood parameter is set to 0.2, and MinPts is set to 5, after clustering is completed, a point which cannot be clustered into a cluster is called a noise point, a CC track is displayed, and a generated cluster is represented by different symbols; areas with high curvature and dense CC points are clustered into the same cluster.
Calculating a coarse grid corresponding to the cutter contact point according to the obtained clustering family, and optimizing a cutter shaft of the coarse grid point based on the coarse grid; meanwhile, fine grids are established between two adjacent coarse grid points, and the cutter shaft of the fine grid points is optimized based on each fine grid, so that the optimization of the cutter shaft is completed.
Referring to fig. 6 and 7, the calculation of the coarse mesh specifically includes the following steps:
and S3.1, replacing the samples in the obtained clustering group division C with the sequences corresponding to the samples.
S3.2, setting the initial traversal times i to be 1, wherein the maximum value in each cluster is MaxiMinimum value of MiniThe number of elements is NumiThe initial Grid division is { G ═ G }1,Gn}，G1Is the sequence of the first CC site, GnThe sequence of the last CC site.
And S3.3, judging whether i is not greater than k, if so, turning to the step S3.4, otherwise, turning to the step S3.8.
S3.4, calculating a clustering cluster CiThe most important ofSmall value MiniMax, MaxiCalculating Grid ∪ { Min ═ Gridi,Maxi}。
S3.5, judging Maxi-MiniIf n is true, go to step S3.6 if yes, otherwise go to step S3.7.
S3.6, clustering the clusters CiSorting in ascending order, traversing CiFinding two discontinuous sequence indexes1And Index2And calculate Grid ∪ { Index ═ Grid1,Index2}。
S3.7, let i ═ i +1, and go to step S3.3.
S3.8, performing ascending sequencing on the Grid to obtain a Grid sequence Grid (g)1,g2,...,gp}。
S3.9, processing grid sequence Grindidex ═ g1,g2,...,gpThe consecutive grid sequence in (1). When i 2, 3.., p-1, all g-satisfying are calculated and removedi-g i-11 and gi+1-giNot equal to 1 and gi-gi-1Not equal to 1 and gi+1-giGrid sequence g formed simultaneously with 1iTo obtain the final coarse grid
Figure BDA0002040974080000091
Referring to fig. 8, 9 and 10, the arbor based on the coarse grid optimized coarse grid point is performed by using an arbor optimization model, where the expression of the arbor optimization model is:
Figure BDA0002040974080000101
Figure BDA0002040974080000102
Figure BDA0002040974080000103
wherein the content of the first and second substances,
Figure BDA0002040974080000104
representing coarse grid points
Figure BDA0002040974080000105
The cutter shaft is arranged at the position of the cutter shaft,
Figure BDA0002040974080000106
representing coarse grid points
Figure BDA0002040974080000107
The cutter shaft is located, w is a weight coefficient,
Figure BDA0002040974080000108
representing coarse grid points
Figure BDA0002040974080000109
And coarse grid points
Figure BDA00020409740800001010
A measure of the distance between the two,
Figure BDA00020409740800001011
representing coarse grid points
Figure BDA00020409740800001012
The preferred direction of the knife shaft is,
Figure BDA00020409740800001013
representing coarse grid points
Figure BDA00020409740800001014
The preferred direction of the knife shaft is,
Figure BDA00020409740800001015
indicating cutter shaft
Figure BDA00020409740800001016
Is located at the minimum boundary of the anteversion angle range of (1),
Figure BDA00020409740800001017
indicating cutter shaft
Figure BDA00020409740800001018
Is located at the maximum boundary of the anteversion angle range,
Figure BDA00020409740800001019
is a knife shaft
Figure BDA00020409740800001020
The forward inclination angle of the arm is smaller than the forward inclination angle of the arm,
Figure BDA00020409740800001021
is a knife shaft
Figure BDA00020409740800001022
Const denotes a constant.
And calculating the chord length of the coarse grid points when the cutter shaft is optimized by adopting the following formula:
Figure BDA00020409740800001023
wherein lk,k+1Representing the euclidean distance between adjacent CC points.
In the present embodiment, take
Figure BDA00020409740800001024
And (5) const is 0, w is 4, the preferable direction of the cutter shaft of the head cutter shaft and the tail cutter shaft is fixed, and then the cutter shaft optimization model is solved by using a constraint optimization method, so that the cutter shaft at the optimized coarse grid point can be obtained.
At every two adjacent coarse grid points
Figure BDA00020409740800001025
Build a fine grid between
Figure BDA00020409740800001026
Optimizing the cutter shaft at the fine grid point based on each fine grid according to a cutter shaft optimization model, wherein the expression of the cutter shaft optimization model is：
Figure BDA00020409740800001027
Figure BDA00020409740800001028
Figure BDA00020409740800001029
Wherein A isj+1Representing fine grid points CCj+1At the knife shaft, AjIndicates coarse grid point CCjThe cutter shaft is arranged. w is a weight coefficient, and is the same as the value in the optimized coarse grid point cutter shaft optimization model. lj+1，jRepresenting neighbouring fine grid points CCjAnd fine grid point CCj+1Between them, MjRepresenting fine grid points CCjIn the preferred direction of the knife axis, Mj+1Representing fine grid points CCj+1The preferred direction of the knife shaft is,
Figure BDA0002040974080000111
showing the knife axis AjIs located at the minimum boundary of the anteversion angle range of (1),
Figure BDA0002040974080000112
showing the knife axis AjMaximum boundary of anteversion angle range of thetajIs a knife shaft AjThe forward inclination angle of the arm is smaller than the forward inclination angle of the arm,
Figure BDA0002040974080000113
is a knife shaft AjConst denotes a constant.
In the present embodiment, take
Figure BDA0002040974080000114
And (3) setting the optimum direction of the cutter shaft of the head cutter shaft and the tail cutter shaft to be fixed and unchanged, and then solving the cutter shaft optimization model by using a constraint optimization method to obtain the cutter shaft at the optimized fine grid point. Cutter shaft after one fine grid interval is optimizedAs shown in fig. 8; fig. 9 shows the optimized knife axes of all the fine mesh intervals.
Comparing the time of cutter shaft optimization before and after the method is used, the finding shows that when the method provided by the invention is implemented by using C + +, the same processing parameters are set, and the number of processing tracks is controlled to be 20, the cutter shaft optimization time is 28.177 seconds before the method is used, and after the method is used, the cutter shaft optimization time is 11.503 seconds, and the algorithm convergence speed is improved by 59.2%.
Comparing the cutter shaft change rates after the method is used and optimized, the cutter shaft change rates are shown in fig. 10, and the ordinate is the ratio of the included angle of the adjacent cutter shafts to the distance delta l between the adjacent CC points:
Figure BDA0002040974080000115
namely the change rate of the cutter shaft, and the abscissa is a CC point sequence; the method of the invention has no adverse effect on the optimization effect of the cutter shaft and further improves the local effect.
According to the density clustering-based multi-grid cutter shaft optimization method, when the coordinates of the cutter contacts are subjected to standardization processing, the standardization processing with a larger standard deviation is selectively performed, so that the adaptability of an algorithm is ensured, the problem that the clustering result is unreasonable due to unreasonable arc length variation values is solved, and the speed and the robustness are improved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (8)

1. A multi-grid cutter shaft optimization method based on density clustering is characterized in that:
(1) carrying out density clustering on the knife contact points subjected to the standardized processing, and specifically comprising the following steps:
s2.1, based on the tool contact set D ═ { CC ═1,CC2,...,CCnDeterminationNeighborhood parameters {, MinPts }, wherein the parameters represent neighborhood radius, MinPts represents the number of points contained in the neighborhood radius range, and n is the number of contact points; next, a set of core points is initialized
Figure FDA0002533307930000011
S2.2, sample CC when j is 1,2, …, n, respectivelyjField N of(CCj) If | N(CCj) If | ≧ MinPts, the sample CCjAdding core point set omega-omega ∪ (CC)j) In which N is(CCj)＝{CCi∈D|DIST(CCi,CCj)≤}，
Figure FDA0002533307930000012
dis(CCk,CCk+1) Representing the Euclidean distance of adjacent CC points, and the knife contact is called the CC point for short; then, initializing a cluster family number k equal to 0 and initializing an unaccessed sample set equal to D,old＝；
s2.3, judging whether the core point set omega is empty, if not, turning to the step S2.4, otherwise, executing the step S2.6;
s2.4, recording the current sample set which is not visitedoldSelecting a core object o ∈ omega randomly, initializing a queue Q ═ o >, { o } solving the difference set \ o } and assigning value, judging
Figure FDA0002533307930000013
If so, go to step S2.5, otherwise go to step S2.6;
s2.5, taking out the first sample Q in the queue Q, and judging | N(q) | is greater than MinPts, if yes, go to step S2.6, otherwise go to step S2.4;
s2.6, let Δ be N(Q) ∩, adding the samples in the delta into a queue Q, solving the difference set \ delta and assigning to the difference set \ delta, and enabling k to be k +1 to generate a cluster Ck＝old\ f; meanwhile, the difference set omega \ C is solvedkAnd assigning the value to omega, and further outputting clustering division C ═ C1,C2,...,Ck}；
(2) Calculating a coarse grid corresponding to the cutter contact point according to the obtained clustering family, and optimizing a cutter shaft of the coarse grid point based on the coarse grid; meanwhile, fine grids are established between two adjacent coarse grid points, and the cutter shaft of the fine grid points is optimized based on each fine grid, so that the optimization of the cutter shaft is completed.
2. The density clustering-based multi-grid cutter shaft optimization method of claim 1, wherein: the optimization of the tool setting contact comprises the following steps: first, a point set D ═ CC is calculated for each blade contact point CC1,CC2,...,CCnMean and standard deviation of x, y, z axis coordinates Std; then, it is determined whether the variance Std is greater than 1, and if so, the CC point set D is set to { CC ═ CC1,CC2,...,CCnCoordinate according to formula
Figure FDA0002533307930000021
Finishing the standardization, wherein c is a coordinate value before the standardization; v is a normalized coordinate value; otherwise, let v equal const and end, where const is a constant.
3. The density clustering-based multi-grid cutter shaft optimization method of claim 1, wherein: adopting a cutter shaft optimization model to optimize a cutter shaft of a coarse grid point based on the coarse grid, wherein the expression of the cutter shaft optimization model is as follows:
Figure FDA0002533307930000022
Figure FDA0002533307930000023
Figure FDA0002533307930000024
wherein the content of the first and second substances,
Figure FDA0002533307930000025
representing coarse grid points
Figure FDA0002533307930000026
A cutter shaft;
Figure FDA0002533307930000027
representing coarse grid points
Figure FDA0002533307930000028
Positioning a cutter shaft; w is a weight coefficient;
Figure FDA0002533307930000029
representing coarse grid points
Figure FDA00025333079300000210
And coarse grid points
Figure FDA00025333079300000211
A distance measure therebetween;
Figure FDA00025333079300000212
representing coarse grid points
Figure FDA00025333079300000213
The preferred direction of the knife shaft;
Figure FDA00025333079300000214
representing coarse grid points
Figure FDA00025333079300000215
The preferred direction of the knife shaft;
Figure FDA00025333079300000216
indicating cutter shaft
Figure FDA00025333079300000217
The minimum boundary of the anteversion angle range of (1);
Figure FDA00025333079300000218
indicating cutter shaft
Figure FDA00025333079300000219
The maximum boundary of the anteversion angle range of (1);
Figure FDA00025333079300000220
is a knife shaft
Figure FDA00025333079300000221
The forward rake angle of (1);
Figure FDA00025333079300000222
is a knife shaft
Figure FDA00025333079300000223
The roll angle of (d); const denotes a constant.
4. The density clustering-based multi-grid cutter shaft optimization method of claim 3, wherein: and calculating the chord length of the coarse grid points when the cutter shaft is optimized by adopting the following formula:
Figure FDA00025333079300000224
wherein lk,k+1Representing the euclidean distance between adjacent CC points.
5. The density clustering-based multi-grid cutter shaft optimization method of claim 1, wherein: adopting an arbor optimization model to optimize the arbor of the fine grid point based on each fine grid, wherein the expression of the arbor optimization model is as follows:
Figure FDA0002533307930000031
Figure FDA0002533307930000032
Figure FDA0002533307930000033
wherein A isj+1Representing fine grid points CCj+1A cutter shaft; a. thejIndicates coarse grid point CCjPositioning a cutter shaft; w is a weight coefficient; lj+1，jRepresenting neighbouring fine grid points CCjAnd fine grid point CCj+1The euclidean distance between; mjRepresenting fine grid points CCjThe preferred direction of the knife shaft; mj+1Representing fine grid points CCj+1The preferred direction of the knife shaft;
Figure FDA0002533307930000034
showing the knife axis AjThe minimum boundary of the anteversion angle range of (1);
Figure FDA0002533307930000035
showing the knife axis AjThe maximum boundary of the anteversion angle range of (1); thetajIs a knife shaft AjThe forward rake angle of (1);
Figure FDA0002533307930000036
is a knife shaft AjThe roll angle of (d); const denotes a constant.
6. The multi-grid cutter shaft optimization method based on density clustering of claim 5, wherein: wherein the content of the first and second substances,
Figure FDA0002533307930000037
const is 0, w is 4; and the head and tail cutter shafts are fixed in the optimized direction of the cutter shaft, and then the cutter shaft optimization model is solved by using a constraint optimization method to obtain the cutter shaft at the optimized fine grid point.
7. The density clustering based multi-grid cutter shaft optimization method of any one of claims 1 to 6, wherein: the calculation of the coarse grid comprises the following steps:
s3.1, replacing the samples in the obtained clustering group division C with a sequence corresponding to the samples, setting the initial traversal times i to be 1, and setting the maximum value in each clustering group to be MaxiMinimum value of MiniThe number of elements is NumiThe initial Grid division is { G ═ G }1,Gn}，G1Is the sequence of the first CC site, GnIs the sequence of the last CC site;
s3.2, judging whether i is not greater than k, if so, turning to the step S3.3, otherwise, turning to the step S3.6;
s3.3, calculating a clustering cluster CiMin of (1)iMax, MaxiAnd calculates Grid-Grid ∪ { Min ═ Gridi,Maxi}; at the same time, Max is judgedi-MiniIf n is true, go to step S3.4 if yes, otherwise go to step S3.5;
s3.4, clustering the clusters CiSorting in ascending order, traversing CiFinding two discontinuous sequence indexes1And Index2And calculate Grid ∪ { Index ═ Grid1,Index2}；
S3.5, let i ═ i +1, and go to step S3.2;
s3.6, and meanwhile, performing ascending sequencing on the Grid to obtain a Grid sequence Grid (g) of the Grid sequence1,g2,...,gp}；
S3.7, processing grid sequence Grindidex ═ g1,g2,...,gpThe sequence of successive grids in (c) to obtain a final coarse grid
Figure FDA0002533307930000041
8. The density clustering-based multi-grid cutter shaft optimization method of claim 7, wherein: when i 2, 3.., p-1, all g-satisfying are calculated and removedi-gi-11 and gi+1-giNot equal to 1 and gi-gi-1Not equal to 1 and gi+1-giGrid sequence g formed simultaneously with 1iTo obtain the final coarse grid
Figure FDA0002533307930000042
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